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4 April 2022 Ultrasound tomography as a gauge invariant fully connected convolutional neural network: repercussions
James W. Wiskin
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Proceedings Volume PC12038, Medical Imaging 2022: Ultrasonic Imaging and Tomography; PC1203806 (2022) https://doi.org/10.1117/12.2610822
Event: SPIE Medical Imaging, 2022, San Diego, California, United States
Abstract
Full wave 3D ultrasound tomography (3D-UT) is shown to be exactly congruent and ‘dual’ to training a gauge equivariant convolutional deep neural network (cDNN) with Lie group SO(2)xR applied to the weights (not feature vectors) and unusual ‘activation functions’. This explains high efficiency on NIVIDIA GPUs and indicates cross application of techniques from 3D-UT to cDNN and vice versa. ‘Backpropagation’ in both arenas is mathematically similar and the weights of the cDNN are the resulting image in 3D-UT. Data acquisition (DA) scenarios are interpreted as mappings from the Lie group manifold, and the 2-sphere, to the N-torus, with ramifications.
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James W. Wiskin "Ultrasound tomography as a gauge invariant fully connected convolutional neural network: repercussions", Proc. SPIE PC12038, Medical Imaging 2022: Ultrasonic Imaging and Tomography, PC1203806 (4 April 2022); https://doi.org/10.1117/12.2610822
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KEYWORDS
Ultrasound tomography
Convolutional neural networks
3D imaging standards
Evolutionary algorithms
Image transmission
Neural networks
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